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Super complete-antimagicness of Amalgamation of any Graph

( Vol-4,Issue-5,May 2017 ) OPEN ACCESS
Author(s):

R.M Prihandini,Ika Hesti Agustin, Dafik, Ridho Alfarisi

Keywords:

Super H-antimagic total graph, Amalgamation of graph, arithmetic sequence.

Abstract:

Let H_i be a finite collection of simple, nontrivial andundirected graphs and let each H_i have a fixed vertex v_jcalled a terminal. The amalgamation H_i as v_j as a terminal isformed by taking all the H_i's and identifying their terminal.When H_(i )are all isomorphic graphs, for any positif integer nwe denote such amalgamation by G=Amal(H,v,n), where ndenotes the number of copies of H. The graph G is said to be an(a,d)-H-antimagic total graph if there exist a bijectivefunction f: V(G)∪ E(G)→ {1,2,… ,|V (G)| +|E(G)|} such that for all subgraphs isomorphic to H, the totalH-weights W(H)=∑_(v∈ V(H)) f(v)+∑_(e∈ E(H)) f(e) forman arithmetic sequence {a,a + d,a +2d,...,a+(n - 1)d}, wherea and d are positive integers and n is the number of allsubgraphs isomorphic to H. An (a,d)-H-antimagic total labelingfis called super if the smallest labels appear in the vertices.In this paper, we study a super (a,d)-H antimagic totallabeling of G=Amal(H,v,n) and its disjoint union.

ijaers doi crossref DOI:

10.22161/ijaers.4.5.32

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